Rewrite as a simplified fraction. ${2.\overline{6} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}10x &= 26.6666...\\ 1x &= 2.6666...\end{align*}}$ Subtracting the two equations, we have: ${9x = 24}$ ${x = \dfrac{24}{9}} $ ${x = \dfrac{8}{3}} \text{or} {2 \dfrac{2}{3}}$